You wrote: "The karmapas, whose rank is second only to the Dalai Lama,..." It hints to a very common misconception, and I think it is important for the sake of accuracy to take care of these matters. There is no such thing like comparative rankings between different sect in Tibetan Buddhism or a central head of all 4 major traditions...
Therefore, it is not possible to say that one of the two is ranking higher or lower.
hence, in the same way as the Dalai Lama isn't the spiritual head of all Buddhists, he is also not the head of all Tibetan Buddhists, and in fact not even the spiritual head of his own school.

The spiritual head of the Gelugpa or Gandenpa is the Ganden Tri Rinpoche, who is regarded as placeholder of the founder of the school, Tsongkhapa.

The Dalai Lama, though, is one of the major Tulkus within his school and his position was also aligned with the position of a worldly, political leadership over Central Tibet before the Chinese invasion.

Furthermore, you wrote:"The two claimants have been kept apart by New Delhi, fearful of upsetting the fragile peace. " In order to do justice to the Indian state, I think it needs to be stated that a legal battle over the main monastery in Rumtek is going on, already at the level of the high court.

The fraction which is occupying the monastery at the moment seems to be losing this battle, and hence New Delhi can of course not allow any of the claimants to occupy the seat in such a situation. Personally, as a follower of the sect, I'm very sorry about these developments and I hope it won't lead to too many people giving up trust in Buddhism as a whole.

In times like these, I think it is good to remember, that the Buddha instructed us to rely on his teachings and not on the individual. It is a path everyone has to go on his own, without getting too much carried away by involving in the political situations he/she encounters.